Opposing the White House on trade is one thing. But don't expect Nancy Pelosi to line up behind Elizabeth Warren and demand President Barack Obama get tougher on Wall Street.

"There may have been a couple of people who say that, but that is not the consensus in our party," Pelosi said in a 45-minute interview. On the charge that the administration has been "too soft" on Wall Street, she added: "The financial industry doesn't agree with that."

Her comment was a reminder that, as the leader of House Democrats, Pelosi outranks Warren despite all the attention the Massachusetts senator has attracted lately for blocking an Obama appointment to the Treasury and slamming Securities and Exchange Commission Chair Mary Jo White. Pelosi joined Warren in the vain attempt to stop Congress from giving the president enhanced authority to negotiate an Asian trade deal.

Nancy Pelosi

Mary Stevens | CNBC

In some ways, the House leader's comment was unsurprising. Pelosi is a prodigious fundraiser who needs some Wall Street backing for her effort to recapture a Democratic majority. She also was the speaker who pushed through the Dodd-Frank Wall Street regulation bill that Warren wishes had been tougher.

(Pelosi spokesman Drew Hammill e-mailed to call the reference to her fundraising "really unfair" because "It implies that her comments on a policy issue are tied to her fundraising...Nobody has been tougher on Wall Street—in ACTUALLY legislating—than Pelosi.")

More broadly, it reflects Pelosi's historic partnership with Obama, despite their divergence on trade. Together the first woman House speaker and first black president won enactment of the national health care law other Democrats had sought unsuccessfully for decades. That law appears more firmly established than ever in the wake of last week's Supreme Court decision.

"I'm very, very proud of the Affordable Care Act," she said. "Nearly 17 million people have health insurance who (otherwise) would not. Seventy million have access to preventive care who would not. Over 100 million people will now not have lifetime limits on what their insurance covers."

"It's Social Security, Medicare and the Affordable Care Act," she concluded. "It's here to stay."

That's only one of the landmark victories she's seen during more than three decades in politics. Another, completed with a Supreme Court ruling last week, was the battle to win gay marriage rights. Pelosi has been a longtime supporter of the cause, even when public opinion was strongly opposed.

"I always said to people, 'Pay attention to what we're saying because you will be saying it sometime soon,' " she said, referring to Republican opposition. Noting continued GOP resistance now that the cause has rocketed up in popularity, she added, "That's really their problem. It's our pride."

Pelosi's problem at the moment is that, even as the nation moves in her party's direction on cultural issues, Democrats face a tougher battle than ever in winning back the House. The most recent reapportionment of congressional districts packed more and more Democratic votes into fewer and fewer districts, which is why Republicans retained a strong majority in 2012 even as House Democratic candidates received more votes nationally. Some election experts believe Democrats are unlikely to win back the House within the next decade.

"I don't necessarily subscribe to that," she said, noting the strengths that Hillary Clinton could bring to the 2016 Democratic ticket. "We have people who want to run. They believe they can win. It's a presidential year—that makes a difference."

In addition to winning back the majority, Pelosi said she wants to keep fighting for congressional action on climate change. That's one issue on which she and Obama hit a wall.

Their effort to pass a cap-and-trade bill regulating carbon emission faltered in the Senate in 2010 before Democrats lost control of Congress, and with it any chance of reviving that proposal. That has left Obama to seek carbon curbs through executive action, even as some Democrats on Capitol Hill try to lay the groundwork for more powerful steps such as a carbon tax.

"It's a fight we have to make. The thermal management of the planet is existential," she said. "Our colleagues are in denial."